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Probingmillicharge@electroncolliders
ZuoweiLiu
NanjingUniversity
UniversityofScienceandTechnologyofChinaMarch25,2021
1
Millichargeisaverysmallelectriccharge
e Qf Aγμ f̄ γμ f
photon
2
Millichargeisaverysmallelectriccharge
u c t
d s b
νe νμ ντ
e μ τ
γ
g
Z
H
W
e Qf Aγμ f̄ γμ f
photon
2
Millichargeisaverysmallelectriccharge
u c t
d s b
νe νμ ντ
e μ τ
γ
g
Z
H
W
Q = 0e Qf Aγ
μ f̄ γμ f
photon
2
Millichargeisaverysmallelectriccharge
u c t
d s b
νe νμ ντ
e μ τ
γ
g
Z
H
W
Q =23
Q = − 1
Q = −13
Q = 0e Qf Aγ
μ f̄ γμ f
photon
2
Millichargeisaverysmallelectriccharge
u c t
d s b
νe νμ ντ
e μ τ
γ
g
Z
H
W
Q =23
Q = − 1
Q = −13
Q = 0e Qf Aγ
μ f̄ γμ f
is quantized in SMQf =n3
photon
2
Millichargeisaverysmallelectriccharge
u c t
d s b
νe νμ ντ
e μ τ
γ
g
Z
H
W
Q =23
Q = − 1
Q = −13
Q = 0e Qf Aγ
μ f̄ γμ f
is quantized in SMQf =n3
non-quantized Qf ≡ ϵ ≪ 1 millicharge
photon
2
Magneticmonopoleleadstochargequantization
[fromh<ps://inspirehep.net/]
Dirac’spaperonmagneFcmonopole&chargequanFzaFonin1931
3
Magneticmonopoleleadstochargequantization
[fromh<ps://inspirehep.net/]
e =2πℏn
μmagneFcmonopole
chargequanFzaFon
ismagneFcstrengthμ
iselectricstrengthe
isintegern
Dirac’spaperonmagneFcmonopole&chargequanFzaFonin1931
3
Standardmodel&grandunifiedtheories
“chargequanFzaFon”isnotresolvedcompletelyinSM
SU(3)c × SU(2)L × U(1)Y
4
Standardmodel&grandunifiedtheories
“chargequanFzaFon”isnotresolvedcompletelyinSM
SU(3)c × SU(2)L × U(1)Y
Embeddedintoabiggergaugegroup,e.g.SU(5) [Georgi&Glashow,PRL.32.438,1974]
chargequanFzaFon
4
StringentconstraintsonmillichargeinSM
[Marinellietal.1984]
[Bressietal.2011]
[Baumannetal.1988]
[Barbiellinietal.1987]
Qp − Qe < (0.8 ± 0.8) × 10−21e
Qn < (−0.1 ± 1.1) × 10−21e
Qn < (−0.4 ± 1.1) × 10−21e
Qν < 10−17e
[Siemensenetal.,PRD97,052004(2018)]
5
MillichargeinBSMcanbequite“large”
[Jaeckel&Ringwald,1002.0329] e ϵ Aγμ χ̄ γμ χ
log10(mχ /eV)
log 1
0(ϵ)
6
MillichargeinBSMcanbequite“large”
[Jaeckel&Ringwald,1002.0329] e ϵ Aγμ χ̄ γμ χ
log10(mχ /eV)
log 1
0(ϵ)
astro/cosmo6
log 1
0(ϵ)
log10(mχ /eV)
MillichargeinBSMcanbequite“large”
[Jaeckel&Ringwald,1002.0329] e ϵ Aγμ χ̄ γμ χ
log10(mχ /eV)
log 1
0(ϵ)
significant allowedϵ
astro/cosmo6
log 1
0(ϵ)
log10(mχ /eV)
Probingmillichargeatelectroncolliders
7
log 1
0(ϵ)
log10(mχ /eV)
Probingmillichargeatelectroncolliders
0.1-10GeV
accessibleatelectroncolliders
BaBarBESIIIBelleIISTCF
7
MillichargedDMexplainsEDGES21cmanomaly
[EDGES2018]
8
MillichargedDMexplainsEDGES21cmanomaly
coldergasorhoYerCMBthanexpected
[EDGES2018]
8
MillichargedDMexplainsEDGES21cmanomaly
coldergasorhoYerCMBthanexpected
[EDGES2018]
MillichargedDMxsec
σ ∝ v−4
easiertoevadeearlyuniverseconstraints
DMcancoolgas
8
Outline:discussionsonmillicharge
[Feldman,ZL,Nath,hep-ph/0702123,299cites]
1 theoreFcalmodels
2 terrestrialsearches
3 electroncolliders’sensiFvity[ZL,Zhang,1808.00983]
[Liang,ZL,Ma,Zhang,1909.06847]
9
1 theoreFcalmodels
[Feldman,ZL,Nath,hep-ph/0702123,299cites]
10
Modelstogeneratemillichargedparticles(MCPs)
[Feldman,ZL,Nath,hep-ph/0702123,299cites]
KineFcmixing
Massmixing
e ϵ Aγμ χ̄ γμ χ is MCPχ
11
Modelstogeneratemillichargedparticles(MCPs)
[Feldman,ZL,Nath,hep-ph/0702123,299cites]
KineFcmixing
Massmixing
e ϵ Aγμ χ̄ γμ χ is MCPχ
11
KineticmixingbetweentwoU(1)fields
ℒ = −14
F2μνFμν2 −
δ2
F2μνFμν1 −
14
F1μνFμν1
KineFcmixingbetweentwoU(1)fields: &A1 A2
[Foot&He,Phys.Le<.267B,509(1991)]
12
[Holdom,Phys.Le<.166B,196(1986)]
KineticmixingbetweentwoU(1)fields
ℒ = −14
F2μνFμν2 −
δ2
F2μνFμν1 −
14
F1μνFμν1
KineFcmixingbetweentwoU(1)fields: &A1 A2
[Foot&He,Phys.Le<.267B,509(1991)]
δ
e−
e+
γ γ′
χ̄
χ
standardmodel
hiddensector
12
[Holdom,Phys.Le<.166B,196(1986)]
KineticmixingbetweentwoU(1)fields
ℒ = −14
F2μνFμν2 −
δ2
F2μνFμν1 −
14
F1μνFμν1
KineFcmixingbetweentwoU(1)fields: &A1 A2
[Foot&He,Phys.Le<.267B,509(1991)]
δ
e−
e+
γ γ′
χ̄
χ
standardmodel
hiddensector
12
millicharge ∼ δ
[Holdom,Phys.Le<.166B,196(1986)]
Oneexampletogeneratekineticmixing
2highscalefermionschargedundertwoU(1)s
[Holdom,Phys.Le<.166B(1986)196-198]
13
Oneexampletogeneratekineticmixing
2highscalefermionschargedundertwoU(1)s
[Holdom,Phys.Le<.166B(1986)196-198]
ℒ = −14
F2μνFμν2 −
14
F1μνFμν1 −
δ2
F2μνFμν1
δ =e1e2
6π2ln
m′ 12
m12
13
Modelstogeneratemillichargedparticles(MCPs)
KineFcmixing
Massmixing
14
StueckelbergmassmixingbetweentwoU(1)fields
ℒ = −14
F2μνFμν2 −
12
(∂μσ + M1A1μ + M2A2μ)2 −14
F1μνFμν1
StueckelbergmassmixingbetweentwoU(1)fields: &A1 A2[Kors&Nathhep-ph/0402047]
[Cheung&Yuanhep-ph/0701107][Feldman,ZL,Nath,hep-ph/0603039]
15
StueckelbergmassmixingbetweentwoU(1)fields
ℒ = −14
F2μνFμν2 −
12
(∂μσ + M1A1μ + M2A2μ)2 −14
F1μνFμν1
StueckelbergmassmixingbetweentwoU(1)fields: &A1 A2[Kors&Nathhep-ph/0402047]
ϵ
e−
e+
γ γ′
χ̄
χ
standardmodel
hiddensector
ϵ ∼M2
M1≪ 1
[Cheung&Yuanhep-ph/0701107][Feldman,ZL,Nath,hep-ph/0603039]
15
StueckelbergmassmixingbetweentwoU(1)fields
ℒ = −14
F2μνFμν2 −
12
(∂μσ + M1A1μ + M2A2μ)2 −14
F1μνFμν1
StueckelbergmassmixingbetweentwoU(1)fields: &A1 A2[Kors&Nathhep-ph/0402047]
ϵ
e−
e+
γ γ′
χ̄
χ
standardmodel
hiddensector
ϵ ∼M2
M1≪ 1
[Cheung&Yuanhep-ph/0701107][Feldman,ZL,Nath,hep-ph/0603039]
15
millicharge ∼ ϵ
“Toy”modelw/bothkinetic&massmixings
−14
F1μνFμν1 −
14
F2μνFμν2 −
δ2
F1μνFμν2 +J′ μAμ
1 +JμAμ2 −
12
M21 A1μAμ
1 −12
M21ϵ2A2μAμ
2 −M21ϵA1μAμ
2
[Feldman,ZL,Nath,hep-ph/0702123,299cites]
16
[Fabbrichesietal.,2005.01515,TheDarkPhoton,p7-9]
“Toy”modelw/bothkinetic&massmixings
−14
F1μνFμν1 −
14
F2μνFμν2 −
δ2
F1μνFμν2 +J′ μAμ
1 +JμAμ2 −
12
M21 A1μAμ
1 −12
M21ϵ2A2μAμ
2 −M21ϵA1μAμ
2
[Feldman,ZL,Nath,hep-ph/0702123,299cites]
1
1 − 2δϵ + ϵ2 ( ϵ − δ
1 − δ2Jμ+
1 − δϵ
1 − δ2J′ μ) Aμ
M +1
1 − 2δϵ + ϵ2 (Jμ − ϵJ′ μ) Aμγ
a_erfieldredefiniFon&rotaFon canonical &diagonalmassmatrix⟶ (−F2/4)
16
[Fabbrichesietal.,2005.01515,TheDarkPhoton,p7-9]
“Toy”modelw/bothkinetic&massmixings
−14
F1μνFμν1 −
14
F2μνFμν2 −
δ2
F1μνFμν2 +J′ μAμ
1 +JμAμ2 −
12
M21 A1μAμ
1 −12
M21ϵ2A2μAμ
2 −M21ϵA1μAμ
2
[Feldman,ZL,Nath,hep-ph/0702123,299cites]
1
1 − 2δϵ + ϵ2 ( ϵ − δ
1 − δ2Jμ+
1 − δϵ
1 − δ2J′ μ) Aμ
M +1
1 − 2δϵ + ϵ2 (Jμ − ϵJ′ μ) Aμγ
a_erfieldredefiniFon&rotaFon canonical &diagonalmassmatrix⟶ (−F2/4)
SM photon
16
[Fabbrichesietal.,2005.01515,TheDarkPhoton,p7-9]
“Toy”modelw/bothkinetic&massmixings
−14
F1μνFμν1 −
14
F2μνFμν2 −
δ2
F1μνFμν2 +J′ μAμ
1 +JμAμ2 −
12
M21 A1μAμ
1 −12
M21ϵ2A2μAμ
2 −M21ϵA1μAμ
2
[Feldman,ZL,Nath,hep-ph/0702123,299cites]
1
1 − 2δϵ + ϵ2 ( ϵ − δ
1 − δ2Jμ+
1 − δϵ
1 − δ2J′ μ) Aμ
M +1
1 − 2δϵ + ϵ2 (Jμ − ϵJ′ μ) Aμγ
a_erfieldredefiniFon&rotaFon canonical &diagonalmassmatrix⟶ (−F2/4)
dark photon SM photon
16
[Fabbrichesietal.,2005.01515,TheDarkPhoton,p7-9]
“Toy”modelw/bothkinetic&massmixings
−14
F1μνFμν1 −
14
F2μνFμν2 −
δ2
F1μνFμν2 +J′ μAμ
1 +JμAμ2 −
12
M21 A1μAμ
1 −12
M21ϵ2A2μAμ
2 −M21ϵA1μAμ
2
[Feldman,ZL,Nath,hep-ph/0702123,299cites]
1
1 − 2δϵ + ϵ2 ( ϵ − δ
1 − δ2Jμ+
1 − δϵ
1 − δ2J′ μ) Aμ
M +1
1 − 2δϵ + ϵ2 (Jμ − ϵJ′ μ) Aμγ
a_erfieldredefiniFon&rotaFon canonical &diagonalmassmatrix⟶ (−F2/4)
degeneracy dark photon SM photon
16
[Fabbrichesietal.,2005.01515,TheDarkPhoton,p7-9]
“Toy”modelw/bothkinetic&massmixings
−14
F1μνFμν1 −
14
F2μνFμν2 −
δ2
F1μνFμν2 +J′ μAμ
1 +JμAμ2 −
12
M21 A1μAμ
1 −12
M21ϵ2A2μAμ
2 −M21ϵA1μAμ
2
[Feldman,ZL,Nath,hep-ph/0702123,299cites]
1
1 − 2δϵ + ϵ2 ( ϵ − δ
1 − δ2Jμ+
1 − δϵ
1 − δ2J′ μ) Aμ
M +1
1 − 2δϵ + ϵ2 (Jμ − ϵJ′ μ) Aμγ
a_erfieldredefiniFon&rotaFon canonical &diagonalmassmatrix⟶ (−F2/4)
degeneracy dark photon SM photon
mass mixing millicharge→
16
[Fabbrichesietal.,2005.01515,TheDarkPhoton,p7-9]
“Realistic”modelw/bothkinetic&massmixings
[Feldman,ZL,Nath,hep-ph/0702123,299cites]
17
commonfeatures
hiddenbosonmixw/hypercharge(insteadofphoton)
hiddenbosonphoton-like(darkphoton)
hypercharge-like mA′ ≫ mZ
mA′ ≪ mZ
3by3massmatrix⟹
“Realistic”modelw/bothkinetic&massmixings
[Feldman,ZL,Nath,hep-ph/0702123,299cites]
17
commonfeatures
hiddenbosonmixw/hypercharge(insteadofphoton)
hiddenbosonphoton-like(darkphoton)
hypercharge-like mA′ ≫ mZ
mA′ ≪ mZ
3by3massmatrix⟹
kineFcmixing millicharge&masslessdarkphoton⟹massmixing millicharge&massivedarkphoton⟹
difference
2 terrestrialsearches
18
Twowaysto“detect”millichargedparticles
scinFllaFon/ionizaFon/scaYering
missingenergy
e ϵ Aγμ χ̄ γμ χ is MCPχ
[ZL,Zhang,1808.00983]
[Liang,ZL,Ma,Zhang,1909.06847]19
Twowaysto“detect”millichargedparticles
scinFllaFon/ionizaFon/scaYering
missingenergy
e ϵ Aγμ χ̄ γμ χ is MCPχ
[ZL,Zhang,1808.00983]
[Liang,ZL,Ma,Zhang,1909.06847]19
SLACmQ:electronbeamdumpexperiment
[Prinzetal,PRL81.1175,1998]
20
SLACmQ:electronbeamdumpexperiment
electron beam
[Prinzetal,PRL81.1175,1998]
20
SLACmQ:electronbeamdumpexperiment
electron beam
sandstone
[Prinzetal,PRL81.1175,1998]
20
SLACmQ:electronbeamdumpexperiment
electron beam
sandstone
[Prinzetal,PRL81.1175,1998]
ordinary charged particles < 90 m
20
SLACmQ:electronbeamdumpexperiment
electron beam
sandstone
scintillation counter
[Prinzetal,PRL81.1175,1998]
ordinary charged particles < 90 m
20
SLACmQconstraintsonmillicharge
[Prinzetal,PRL81.1175,1998]
21
SLACmQconstraintsonmillicharge
[Prinzetal,PRL81.1175,1998]
m>100MeVMCPyielddieoff
21
MilliQan:proposedscintillationdetector@LHC
[Haasetal.,1410.6816]
22
[Balletal.,1607.04669]
MilliQan:proposedscintillationdetector@LHC
[Haasetal.,1410.6816]plasFc
scinFllatorsarraywith3secFons(poinFngtoCMSIP),each
containing400
scinFllatorbarscoupledtoPMT.33mawayfromCMSIP.
1 m × 1 m × 3 m
5 cm × 5 cm × 80 cm
22
[Balletal.,1607.04669]
MilliQansensitivityonmillichargedparticles
[Balletal.,1607.04669]
23
MilliQansensitivityonmillichargedparticles
[Balletal.,1607.04669]
photoelectrondropsbelowonewhen
ϵ ≲ O(10−3)
23
ArgoNeuT@FermiLab:liquidargoneutrinodetector
[Harniketal.,1902.03246]
24
[ArgoNeuT,1911.07996]
ArgoNeuT@FermiLab:liquidargoneutrinodetector
[Harniketal.,1902.03246]
NuMI target
24
[ArgoNeuT,1911.07996]
ArgoNeuT@FermiLab:liquidargoneutrinodetector
[Harniketal.,1902.03246]
NuMI targetLiquid argon time
projection chamber
24
[ArgoNeuT,1911.07996]
LimitsfromArgoNeuT&MilliQandemonstrator(1%)
[ArgoNeuT,1911.07996]
ArgoNeuT POT1020
25
LimitsfromArgoNeuT&MilliQandemonstrator(1%)
[milliQandemonstrator,2005.06518]
1%oftotaldetector
37/iin2018
[ArgoNeuT,1911.07996]
ArgoNeuT POT1020
25
MCPscattersw/neutrinoexperimenttarget
MCP produced in proton fixed-target experiments
MCP scatters w/ target (electron) in the neutrino detector
[Magilletal.,1806.03310]
solid:datadashed:projecFon
26
Somefutureexperimentsonmillicharge(incomplete)
LDMX:electronfixedtarget
FerMINI:scinFllators@protonfixedtarget
NA64:muonfixedtarget
SUBMET:scinFllators@JPARC
neutrinoexperiments
DMexperiments
27
3 electroncolliders’sensiFvity
[ZL,Zhang,1808.00983]
[Liang,ZL,Ma,Zhang,1909.06847]
28
log 1
0(ϵ)
log10(mχ /eV)
Probingmillichargeatelectroncolliders
0.1-10GeV
accessibleatelectroncolliders
BaBarBESIIIBelleIISTCF
[ZL,Zhang,1808.00983][Liang,ZL,Ma,Zhang,1909.06847]
29
log 1
0(ϵ)
log10(mχ /eV)
Probingmillichargeatelectroncolliders
0.1-10GeV
accessibleatelectroncolliders
BaBarBESIIIBelleIISTCF
[ZL,Zhang,1808.00983][Liang,ZL,Ma,Zhang,1909.06847]
inabilityofthedetectors
missingenergy
29
Processtosearchformillichargedparticles
verysmallionizaFonsignalfrommillicharge
mono-photon@electroncolliders
[ZL,Zhang,1808.00983]
30
Processtosearchformillichargedparticles
verysmallionizaFonsignalfrommillicharge
mono-photon@electroncolliders
e−
e+
e
γ
χ̄
χ
γ
γ
[ZL,Zhang,1808.00983]
30
Processtosearchformillichargedparticles
verysmallionizaFonsignalfrommillicharge
mono-photon@electroncolliders
e−
e+
e
γ
χ̄
χ
γ
γ
[ZL,Zhang,1808.00983]
millicharge vertex: e ϵ Aγμ χ̄ γμ χ
30
Processtosearchformillichargedparticles
verysmallionizaFonsignalfrommillicharge
mono-photon@electroncolliders
e−
e+
e
γ
χ̄
χ
γ
γ
[ZL,Zhang,1808.00983]
millicharge vertex: e ϵ Aγμ χ̄ γμ χ
“invisible”atelectroncolliders
30
Processtosearchformillichargedparticles
verysmallionizaFonsignalfrommillicharge
mono-photon@electroncolliders
e−
e+
e
γ
χ̄
χ
γ
γ
[ZL,Zhang,1808.00983]
millicharge vertex: e ϵ Aγμ χ̄ γμ χ
monophoton
“invisible”atelectroncolliders
30
IrreducibleBG(monophotonplus2neutrinos)
e
e
νν
γe
Z
e
e
νe
νe
γ
W
e
e
e
νe
νe
γ
W
W
IrreducibleBG:e+e− → γνν
31
IrreducibleBG(monophotonplus2neutrinos)
e
e
νν
γe
Z
e
e
νe
νe
γ
W
e
e
e
νe
νe
γ
W
W
small
IrreducibleBG:e+e− → γνν
31
monophotoncrosssection@electroncolliders
millichargeprocess:e+e-→𝞆𝞆ɣ
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[ZL,Zhang,1808.00983]
32
monophotoncrosssection@electroncolliders
millichargeprocess:e+e-→𝞆𝞆ɣ
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1/2<latexit sha1_base64="hxTRVKmJATh5x2QtM/HKdhDyxDI=">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</latexit><latexit sha1_base64="hxTRVKmJATh5x2QtM/HKdhDyxDI=">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</latexit><latexit sha1_base64="hxTRVKmJATh5x2QtM/HKdhDyxDI=">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</latexit><latexit sha1_base64="hxTRVKmJATh5x2QtM/HKdhDyxDI=">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</latexit>
[ZL,Zhang,1808.00983]
irreducibleBG:e+e-→ɣνν
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#
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f(sW ) = 8s4W � 4s2W /3 + 1<latexit sha1_base64="JHyVl0+zIkoW6by+g9sTDA266Ao=">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</latexit><latexit sha1_base64="JHyVl0+zIkoW6by+g9sTDA266Ao=">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</latexit><latexit sha1_base64="JHyVl0+zIkoW6by+g9sTDA266Ao=">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</latexit><latexit sha1_base64="JHyVl0+zIkoW6by+g9sTDA266Ao=">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</latexit>
sW ⌘ sin ✓W<latexit sha1_base64="F3b5vGIN378EI0G8l9YZeRCNX40=">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</latexit><latexit sha1_base64="F3b5vGIN378EI0G8l9YZeRCNX40=">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</latexit><latexit sha1_base64="F3b5vGIN378EI0G8l9YZeRCNX40=">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</latexit><latexit sha1_base64="F3b5vGIN378EI0G8l9YZeRCNX40=">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</latexit>
[Ma,Okada1978]
[Gaemers+1979]
32
“Low”collidingenergyisbettertoprobeMCPs
2 4 6 8 10 12 14ps (GeV)
10°2
10°1
100
101
102æ
(fb)
Pre-selection Cuts≤ = 0.001
m¬ = 0.1 GeV
irreducible SM BG
ifirreducibleBGistheonlyimportantBG
33
“Low”collidingenergyisbettertoprobeMCPs
2 4 6 8 10 12 14ps (GeV)
10°2
10°1
100
101
102æ
(fb)
Pre-selection Cuts≤ = 0.001
m¬ = 0.1 GeV
irreducible SM BG
e+e− → γ χ̄ χ
ifirreducibleBGistheonlyimportantBG
33
“Low”collidingenergyisbettertoprobeMCPs
2 4 6 8 10 12 14ps (GeV)
10°2
10°1
100
101
102æ
(fb)
Pre-selection Cuts≤ = 0.001
m¬ = 0.1 GeV
irreducible SM BG
e+e− → γ χ̄ χ
e+e− → γ ν̄ ν
ifirreducibleBGistheonlyimportantBG
33
[Chao,Wangetal.0809.1869]
BESIIIdetectors&reducibleBG
beamenergy:1.0-2.3GeV
Maindri_chamber(MDC)
|cos(𝚹ɣ)|<0.93
Time-of-Flight(TOF)
|cos(𝚹ɣ)|<0.83
0.85<|cos(𝚹ɣ)|<0.95
ElectromagnegFccalorimeter(EMC)
|cos(𝚹ɣ)|<0.83
0.85<|cos(𝚹ɣ)|<0.93
34
[Chao,Wangetal.0809.1869]
BESIIIdetectors&reducibleBG
beamenergy:1.0-2.3GeV
Maindri_chamber(MDC)
|cos(𝚹ɣ)|<0.93
Time-of-Flight(TOF)
|cos(𝚹ɣ)|<0.83
0.85<|cos(𝚹ɣ)|<0.95
ElectromagnegFccalorimeter(EMC)
|cos(𝚹ɣ)|<0.83
0.85<|cos(𝚹ɣ)|<0.93
ɣ
e-e+
34
BelleIIhasseveraluncoveredangularregions
7GeVelectroncollidesw/4GeVpositron
35
BelleIIhasseveraluncoveredangularregions
7GeVelectroncollidesw/4GeVpositron
[BelleII1808.10567]
ECLangles(labframe)
12.4∘ < θ < 31.4∘
32.2∘ < θ < 128.7∘
130.7∘ < θ < 155.1∘
35
BelleIIhasseveraluncoveredangularregions
7GeVelectroncollidesw/4GeVpositron
[BelleII1808.10567]
ECLangles(labframe)
12.4∘ < θ < 31.4∘
32.2∘ < θ < 128.7∘
130.7∘ < θ < 155.1∘
35
BelleIIhasseveraluncoveredangularregions
7GeVelectroncollidesw/4GeVpositron
reducibleBGBGduetoECLgaps(gBG)
BGduetobeam(bBG)
[BelleII1808.10567]
ECLangles(labframe)
12.4∘ < θ < 31.4∘
32.2∘ < θ < 128.7∘
130.7∘ < θ < 155.1∘
35
Dark Sectors at Low Energy Colliders (Torben Ferber) �22
Background MC, 40 fb-1 after selection
ee→eeγboth electrons
out of tracking acceptance
ee→2γ and 3γ 1γ in ECL 90° gap
1γ out of ECL acceptance
ee→2γ 1γ in ECL BWD or FWD gap
ee→3γ 1γ in ECL BWD gap
1γ out of ECL acceptance
Belle II MC
Introduction• Dark Photon A’ motivated by Dark Matter, g-2, ..
• Minimal Dark Matter model: Dark Matter particle χ and a new scalar or gauge Boson A’ as s-channel annihilation mediator (mA’ > 2mχ)
• Additional U(1)’ symmetry → Kinetic mixing* of massive Dark Photon with the SM photon
313/28
Towards First Physics: Dark Photon.
>Dark Photon motivated by dark matter, g-2 anomaly...
>Minimal dark matter model: Dark matter particle N and a new scalar or gauge boson A' as s-channel annihilation mediator (mA' > 2mN)
>Additional U(1)' symmetry ? “Kinetic Mixing”* of massive dark photon A' with the SM photon
*Holdom, Phys. Lett B166, 1986
Eγ=s−M A'
2
2√ s
13/28
Towards First Physics: Dark Photon.
>Dark Photon motivated by dark matter, g-2 anomaly...
>Minimal dark matter model: Dark matter particle N and a new scalar or gauge boson A' as s-channel annihilation mediator (mA' > 2mN)
>Additional U(1)' symmetry ? “Kinetic Mixing”* of massive dark photon A' with the SM photon
*Holdom, Phys. Lett B166, 1986
Eγ=s−M A'
2
2√ s
B: Invisible Dark Photon searches
Belle
[takenfromTorbenFerber’stalk]
36
20 40 60 80 100 120 140µ∞
lab (deg)
2
3
4
5
6
E∞ cm
(GeV
)
high-mass
low-massbBG
Belle II
Photonenergyandangularcuts@BelleII
[Liang,Liu,Ma,Zhang,1909.06847]37
20 40 60 80 100 120 140µ∞
lab (deg)
2
3
4
5
6
E∞ cm
(GeV
)
high-mass
low-massbBG
Belle II
Photonenergyandangularcuts@BelleII
bBG
[Liang,Liu,Ma,Zhang,1909.06847]37
20 40 60 80 100 120 140µ∞
lab (deg)
2
3
4
5
6
E∞ cm
(GeV
)
high-mass
low-massbBG
Belle II
Photonenergyandangularcuts@BelleII
bBG
lowmassregion
[BelleII1808.10567]
[Liang,Liu,Ma,Zhang,1909.06847]37
20 40 60 80 100 120 140µ∞
lab (deg)
2
3
4
5
6
E∞ cm
(GeV
)
high-mass
low-massbBG
Belle II
Photonenergyandangularcuts@BelleII
bBG
lowmassregion
[BelleII1808.10567]
[Liang,Liu,Ma,Zhang,1909.06847]
highmassregion
[BelleII1808.10567]
37
electroncollidersprobenewparameterregion(95%CL)
0.001 0.01 0.1 1 4m¬ (GeV)
10°5
10°4
10°3
10°2
10°1
"
Colliders
BaBar 28/fb
BESIII 17/fbBelle II 50/ab
STCF 20/ab
SLAC
√MiniBooNE
√LSND
CMB
ann.
fdm= 10
°2
fdm= 10
°3
ArgoNeuT
NeÆ
Belle II bBG+gBG
Belle II bBG
Belle II optimized
BESIII bBG
STCF bBG
STCF optimized
[Liang,Liu,Ma,Zhang,1909.06847]38
electroncollidersprobenewparameterregion(95%CL)
0.001 0.01 0.1 1 4m¬ (GeV)
10°5
10°4
10°3
10°2
10°1
"
Colliders
BaBar 28/fb
BESIII 17/fbBelle II 50/ab
STCF 20/ab
SLAC
√MiniBooNE
√LSND
CMB
ann.
fdm= 10
°2
fdm= 10
°3
ArgoNeuT
NeÆ
Belle II bBG+gBG
Belle II bBG
Belle II optimized
BESIII bBG
STCF bBG
STCF optimized
[Liang,Liu,Ma,Zhang,1909.06847]
BaBar
38
electroncollidersprobenewparameterregion(95%CL)
0.001 0.01 0.1 1 4m¬ (GeV)
10°5
10°4
10°3
10°2
10°1
"
Colliders
BaBar 28/fb
BESIII 17/fbBelle II 50/ab
STCF 20/ab
SLAC
√MiniBooNE
√LSND
CMB
ann.
fdm= 10
°2
fdm= 10
°3
ArgoNeuT
NeÆ
Belle II bBG+gBG
Belle II bBG
Belle II optimized
BESIII bBG
STCF bBG
STCF optimized
[Liang,Liu,Ma,Zhang,1909.06847]
BaBar
BESIII
38
electroncollidersprobenewparameterregion(95%CL)
0.001 0.01 0.1 1 4m¬ (GeV)
10°5
10°4
10°3
10°2
10°1
"
Colliders
BaBar 28/fb
BESIII 17/fbBelle II 50/ab
STCF 20/ab
SLAC
√MiniBooNE
√LSND
CMB
ann.
fdm= 10
°2
fdm= 10
°3
ArgoNeuT
NeÆ
Belle II bBG+gBG
Belle II bBG
Belle II optimized
BESIII bBG
STCF bBG
STCF optimized
[Liang,Liu,Ma,Zhang,1909.06847]
BaBar
BESIII
BelleII
38
electroncollidersprobenewparameterregion(95%CL)
0.001 0.01 0.1 1 4m¬ (GeV)
10°5
10°4
10°3
10°2
10°1
"
Colliders
BaBar 28/fb
BESIII 17/fbBelle II 50/ab
STCF 20/ab
SLAC
√MiniBooNE
√LSND
CMB
ann.
fdm= 10
°2
fdm= 10
°3
ArgoNeuT
NeÆ
Belle II bBG+gBG
Belle II bBG
Belle II optimized
BESIII bBG
STCF bBG
STCF optimized
[Liang,Liu,Ma,Zhang,1909.06847]
BaBar
BESIII
BelleII
STCF
38
electroncollidersprobenewparameterregion(95%CL)
0.001 0.01 0.1 1 4m¬ (GeV)
10°5
10°4
10°3
10°2
10°1
"
Colliders
BaBar 28/fb
BESIII 17/fbBelle II 50/ab
STCF 20/ab
SLAC
√MiniBooNE
√LSND
CMB
ann.
fdm= 10
°2
fdm= 10
°3
ArgoNeuT
NeÆ
Belle II bBG+gBG
Belle II bBG
Belle II optimized
BESIII bBG
STCF bBG
STCF optimized
[Liang,Liu,Ma,Zhang,1909.06847]
BaBar
BESIII
BelleII
STCF
diffBGconsideraFons
38
electroncollidersprobenewparameterregion(95%CL)
0.001 0.01 0.1 1 4m¬ (GeV)
10°5
10°4
10°3
10°2
10°1
"
Colliders
BaBar 28/fb
BESIII 17/fbBelle II 50/ab
STCF 20/ab
SLAC
√MiniBooNE
√LSND
CMB
ann.
fdm= 10
°2
fdm= 10
°3
ArgoNeuT
NeÆ
Belle II bBG+gBG
Belle II bBG
Belle II optimized
BESIII bBG
STCF bBG
STCF optimized
[Liang,Liu,Ma,Zhang,1909.06847]
BaBar
BESIII
BelleII
STCF
diffBGconsideraFons
newregions:0.1-4GeV
38
electroncollidersprobenewparameterregion(95%CL)
0.001 0.01 0.1 1 4m¬ (GeV)
10°5
10°4
10°3
10°2
10°1
"
Colliders
BaBar 28/fb
BESIII 17/fbBelle II 50/ab
STCF 20/ab
SLAC
√MiniBooNE
√LSND
CMB
ann.
fdm= 10
°2
fdm= 10
°3
ArgoNeuT
NeÆ
Belle II bBG+gBG
Belle II bBG
Belle II optimized
BESIII bBG
STCF bBG
STCF optimized
[Liang,Liu,Ma,Zhang,1909.06847]
BaBar
BESIII
BelleII
STCF
diffBGconsideraFons
?ϵ ≲ O(10−4)
newregions:0.1-4GeV
38
Summary
MillichargedparFclescanappearinkineFcmixingorStueckelbergmassmixingmodels
AnumberofterrestrialexperimentshavebeencarriedoutorproposedtosearchformillichargedparFcles
WeproposetosearchformillichargedparFclesatelectroncolliders,includingBESIII,Belle-IIandSTCF,whichcanprobecurrentlyunexploredparameterregions:ϵ ≲ O(10−3) for 100 MeV ≲ m ≲ several GeV
39
[Feldman,ZL,Nath,hep-ph/0702123,299cites]
[ZL,Zhang,1808.00983][Liang,ZL,Ma,Zhang,1909.06847]
addiFonalslides
40
0.001 0.01 0.10 1 3m¬ (GeV)
10°5
10°4
10°3
"
7 GeV
4 GeV
2 GeV STCF 10/ab
DifferentSTCFcollidingenergies
STCFlow-Emode:beYerforlowmass
41
0.01 0.10 1 5m¬ (GeV)
10°1
100"
High-E
Low-E
BaBar 28/fb
BaBarsensisvityonmillicharge
[BaBar,0808.0017]
High-E3.2 < E⇤
� < 5.5 GeV<latexit sha1_base64="11o7ygJIXiln6j5YnuV4AV0tbUA=">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</latexit>
�0.31 < cos ✓⇤� < 0.6<latexit sha1_base64="U70maJk/dG0auGOVbGqAKupCVAU=">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</latexit>
Low-E2.2 < E⇤
� < 3.7 GeV<latexit sha1_base64="pVADkRPFC44zF9JHX0gDI8gP0yI=">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</latexit>
�0.46 < cos ✓⇤� < 0.46<latexit sha1_base64="HzSE/my43Ds/lV8GU2ebkyOC2RA=">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</latexit>
high-EdatahasbeYersensiFvitytolightmass42
MassgrowthviaStueckelberg
MakemassiveQEDgaugeinvariantbyaddingaxion𝞂
L = �1
4Fµ⌫F
µ⌫ � m2
2A2
µ
=) � 1
4Fµ⌫F
µ⌫ � 1
2(mAµ + @µ�)
2
<latexit sha1_base64="YFG7yL3iWuVFtFI4jeywUNVL3yU=">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</latexit><latexit sha1_base64="YFG7yL3iWuVFtFI4jeywUNVL3yU=">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</latexit><latexit sha1_base64="YFG7yL3iWuVFtFI4jeywUNVL3yU=">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</latexit><latexit sha1_base64="YFG7yL3iWuVFtFI4jeywUNVL3yU=">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</latexit>
�Aµ = @µ�, �� = �m�
invariantundergaugetransformaFon
σ:longitudinalmodeofthevectorboson
[E.C.G.Stueckelberg,Helv.Phys.Acta11,225(1938)]43
Stueckelberginextradimensions
compacFficaFonofa5Dtheoryonhalf-circle
L5 = �1
4Fab(z)F
ab(z), a, b = 0, 1, 2, 3, 5
infinitenumberofmassiveKKmodesin4D
�1
2
X
n
M2n
✓A(n)
µ (x) +1
Mn@µ�
(n)(x)
◆2
L4 = �1
4
X
n
F (n)µ⌫ (x)Fµ⌫(n)(x)
Stueckelbergmassin4DduetocompacFficaFon[Nath0812.0958]
S1/Z2
za = (xµ, y), µ = 0, 1, 2, 3 Aa = (Aµ(z),�(z))
44
StueckelbergvsHiggsU(1)bosonw/aHiggspotenFal
L = �1
4Fµ⌫F
µ⌫ +h(@µ + igAµ)�
i2�
hµ2�⇤�+ �(�⇤�)2
i
DecomposetheHiggsfieldinpolarcoordinates
� =
✓v + hp
2
◆ei
�v v =
r�µ2
�
Unitarygauge �U =v + hp
2
L = �F 2U
4+
(@µh)2
2+
g2
2(h+ v)2AU
µAUµ � �
4(h2 + 2hv)2 +
�
4v4
AUµ = Aµ � 1
gv@µ�&
Mh =p2�v
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MA = gv<latexit sha1_base64="kdcqK2k4uqbklQvoxKC/zJOOXyI=">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</latexit>
𝛔disappears45
decoupletheHiggsparticle
L = �F 2U
4+
M2A
2AU
µAUµ
AUµ = Aµ � 1
MA@µ�
LowenergyeffecFvetheory
L = �F 2µ⌫
4+
1
2(MAAµ � @µ�)
2
TheHiggsmechanismleadstotheStueckelbergmechanism.
[Allen,Bowick,Lahiri,Mod.Phys.Le<.A6,559,(1991)][Nath,arXiv:0812.0958] [Nelson,Scholtz,arXiv:1105.2812]
Take the limits �µ2 ! 1, � ! 1 with v =
p�µ2/� fixed.
In this case, the Higgs field Mh =p2�v becomes infinitely
heavy and decouples, whereas the gauge boson mass
MA = gv remains unchanged.
46